Vol. 117 (2010)
ACTA PHYSICA POLONICA A
No. 6
Dielectric and AC Conductivity
of Potassium Perchlorate, KCLO4
H.M. Abdelmoneim∗
Physics Department, Faculty of Science, Cairo University, Giza, Egypt
(Received November 13, 2008; corrected version October 10, 2009; in final form May 5, 2010)
The AC conductivity σ(ω) and the complex dielectric permittivity ε∗ (ω) were studied as function of
temperature 300 K < T < 600 K and at some selected frequencies (1–20 kHz) for polycrystalline sample of KClO4 .
The differential thermal analysis (DTA) thermograph was also performed. The combined data support each other
and indicate the existence of a structural phase transition at ≈ 575 K. Moreover, the temperature dependence of
the ac conductivity behaves in accordance with Arrhenius relation, whereas the frequency dependent conductivity
obeys the power law σ(ω) = Aω s(T ) . The behavior of s with temperature suggests that the hopping over the
barrier model prevails. No evidence for the existence of a ferroelectric phase transition at the transition temperature.
PACS numbers: 72.80.Ph, 77.22.Ch, 77.84.Bw
1. Introduction
Potassium perchlorate KClO4 is an important member
of monovalent or alkali metal of the general molecular formula MClO4 where M stands for a monovalent metal ion
(M = Cs, Rb, K, Na, and/or NH4 ). On the other hand,
the molecular formula of a related series, namely divalent metal perchlorates is D (ClO4 )2 -xH2 O where D is a
divalent metal ion (D = Zn, Cu, Ca, etc.) and x is the
number of water molecules, i.e., x = 0, 1, 2, . . . All these
perchlorates are salts of perchloric acid which attract the
attention of investigators owing to their interesting properties. For example, most of these compounds undergo
structural phase transitions at high and low temperatures
[1–8]. Furthermore the crystal structures of some members of these series were determined [9–11]. Among other
things one may replace the above mentioned formula by
MhO4 and M(hO4 )2 -xH2 O4 , where h is a halogen atom
(h = Cl, Br, I, . . . ) the other symbol take their usual
meanings. For perbromate compound the crystal structure of LiBrO4 ·3H2 O [12] and [Ca (H2 O)4 ](BrO4 )2 [13]
were also investigated.
For the alkali metals perchlorate with M = Cs, Rb,
and K, the modulus spectroscopy and dielectric dispersion were performed on single crystals prepared by the
gel technique [2]. A high temperature phase transition
was detected around ≈ 302 ◦C (575 K).
Literature survey indicated that there are no reported
data on the type of conduction mechanism in the present
compound. This initiated the motivation behind the
∗
corresponding author; e-mail: [email protected]
present work, where the electrical parameters are determined and presented according to the current style.
This is considered as a continuation of our research program where the dielectrical properties are investigated
as a function of both frequency and temperature [14] for
some selected disordered solids. Furthermore, the confirmation of the structural phase transition in the compound is also one of our objectives.
The starting point is that, the complex dielectric permittivity ε∗ (ω) can be resolved into, the real part ε0 (ω)
and the imaginary part ε00 (ω) according to the equation:
ε∗ (ω) = ε0 (ω) − iε00 (ω)
(1)
Furthermore, the total measured conductivity
σtot (ω, T ) for a wide class of dielectric materials
(semiconductors, organic, inorganic, glass, etc.) shows
dispersion behavior through its dependence on the
frequency (ω) according to Jonsher relation [15]:
σtot (ω, T ) = σ(0, T ) + σac (ω, T ).
(2)
The frequency dependent part σac (ω, T ) follows the
power law:
σac (ω, T ) = A(T )ω s(T ) .
(3)
The above equation is called the power law or universal
dynamic response and is used to analyze the conductivity in all disordered solids [15–29]. In this equation A(T )
and s(T ) are characteristic parameters which are temperature dependent. Of particular interest, is the frequency
exponent whose value lies in the range 0 < s < 1. The
exponent measures the degree of interaction of mobile
ions with the environment [16]. A(T ) determines the polarizability [29]. For Debye type interaction s ≈ 1 and
for pure ionic crystal s ≈ 0, i.e., s decreases with the
increase of interaction. The temperature dependence of
(936)
Dielectric and ac Conductivity of Potassium Perchlorate, KCLO4
s determines, to a large extent, the type of conduction
mechanism.
2. Experiment
The samples used in the present work were supplied
by BDH Laboratory Reagent, the British Drug Houses
LTD., London and manufactured in England (99.9% purity). The polycrystalline powder was compressed under
a suitable pressure to form discs (pellets) of about 1 cm
diameter and 1–2 mm thickness, and good contact was
obtained by painting both faces of sample with air-drying
conducting silver paste. A sample holder with brass electrodes was especially designed to fit the present measurements. The sample holder was inserted into an electric
furnace which is connected to a temperature controlled
ac-variac. The electrical parameters (R, C and Z) were
measured using a digital RLC bridge Philips PM6304.
Data were collected for at least three samples and the results were found to be quite consistent and reproducible.
The measured values of R, C and Z at different temperature and frequency were converted into AC-conductivity
σac and relative permittivity ε0 , using the area and the
thickness measurements of the pellet by using a simple
program where the bridge is interfaced with a computer.
All measurements were carried out at thermal equilibrium. Calibration, using standard material is usually
performed before any actual measurements. The experimental errors of both σac and ε0 are lower than ±3%.
2.1. Electrical parameters
2.1.1. Dielectric permittivity
The temperature dependence of the real part ε0 of the
complex dielectric permittivity measured in the temperature range 300 K < T < 600 K and at different frequencies 1–20 kHz is shown in Fig. 1. As one can see, the value
of ε0 (for frequencies higher than 5 kHz) is nearly temperature independent up to ≈ 560 K, beyond which, the
value of ε0 decreases to a minimum value at T ≈ 575 K
then it starts to increase again with temperature. This
behavior of ε0 vs. T , suggests the existence of some sort
of structural phase transition at this particular temperature.
Fig. 1. Temperature and frequency dependence of the
real part ε0 of the dielectric permittivity.
937
The dependence of ε0 on the frequency in the same
temperature interval is shown in Fig. 2. For the purpose
of clarity only selected temperatures are chosen. The
general feature of the plot is that the dispersion increases
with increasing temperature and decreasing frequency in
accordance with the typical behavior of the dielectric.
Fig. 2.
Relation between ε0 versus ln(f ).
Fig. 3. Variation of the imaginary part ε00 of the dielectric permittivity as function of temperature measured at
different frequencies.
Figure 3 shows the variation of the imaginary part
ε00 with temperature measured in the same frequency
range 1–20 kHz. The general feature of this plot is that,
the value of ε00 is almost temperature independent and
also frequency independent in the interval 300 K < T <
480 K. However, as the temperature exceeds 500 K, the
loss factor ε00 increases. Another point of interest is the
existence of a kink at about T ≈ 575 K, indicating also
the possibility of phase transition and/or a change in the
conduction mechanism.
2.1.2. Electrical conductivity σ(ω),
temperature dependence
The AC conductivity data is usually presented in terms
of an Arrhenius relation:
σac (T ) = σ(0) exp(−Eg /kT ),
(4)
where Eg is the activation energy of the process and the
other terms take their usual meanings.
938
H.M. Abdelmoneim
eral trend of the plot is that there is a gradual increase
in the value of ln A(T ) as the temperature increases.
Fig. 4. Relation between ln(σT ) versus 1000/T at different frequencies.
Figure 4 represents a relation between ln σ(T ) and
1000/T . One can identify two temperature regions designated by I and II, in addition to a limited-pretransition-region.
Region II (300 K > T ≥ 480 K):
This region is characterized by a linear variation of
ln(σ) and 1000/T . Moreover, the value of ln(σac ) (and
hence σac ) is almost temperature independent, but frequency dependent. This behavior reflects an extrinsic
conduction type. The values of Eg are nearly equal. The
more acceptable value is Eg = 0.05 ± 0.01 eV.
Pretransition region (PT) (480 K > T ≥ 575 K):
In this region the change in the conductivity is very
fast and becomes temperature and frequency dependent.
The results show abrupt change in the slope of the curve
compared with region II. In the vicinity and just before
the transition, the conductivity becomes frequency independent. The data in this case are so limited and hence
the value of Eg is not calculated here.
Region I (575 K > T > 630 K):
In this temperature range, the conductivity depends
on both the frequency and the temperature. As one can
see, for a given frequency, the value of ln(σac ) increases
with increasing temperature, and decreases with increasing frequency. The values of the activation energy decrease from 0.55 eV at 1 kHz to 0.3 eV at 20 kHz.
2.1.3. Electrical conductivity σ(ω),
frequency dependence
Figure 5 shows, the double logarithmic plot, i.e.,
ln(σac ) vs. ln(ω). The graph is characterized by a set
of, approximately, straight lines of different slopes in accordance with the universal dynamic response (the power
law, Eq. (3)). The slope of each line gives the value of the
frequency exponent s at the corresponding temperature:
s = [δ ln(σac )/δ ln(ω)]
(5)
In Fig. 6, the temperature dependence of s is displayed.
The general behavior of the plot is that s decreases slowly
with increasing temperature and its value is less than
unity. Figure 7 shows the variation of parameter A(T )
with temperature plotted as ln(A(T )) versus T . The gen-
Fig. 5.
Double logarithmic plot (ln(σ) vs. ln(ω)).
Fig. 6. Temperature dependence of frequency exponent s.
Fig. 7. The variation of ln(A(T )) with the temperature T .
2.2. Thermal parameters
The differential thermal analysis (DTA) thermogram
as performed by Shimadzu detector DTA-50 with a heating rate 5 ◦C/min in the temperature range 280 K < T <
Dielectric and ac Conductivity of Potassium Perchlorate, KCLO4
939
σ(ω) = (η/3)e2 kT (N (Ef )T )2 α−5 ω[ln(υph /ω)]4
(6)
where N(Ef ) is the density of states at Fermi level, υph
is the phonon frequency in the order of 1013 sec−1 and α
is the decay of the localized states wave function (α ≈ 1
Å) [16]. The expression that describes the behavior of s,
in the QMT model is given by:
s = 1 − {4/ ln(υph /ω)}
(7)
whereas, for classical hopping:
s = 1 − 6kT /{Eo − kT ln(υph /ω)}
Fig. 8.
The DTA thermogram.
670 K is shown in Fig. 8. The plot is characterized by
a very sharp endothermic peak centered at T ≈ 578 K.
This behavior shows a clear structural phase transition
at ≈ 575 K.
3. Discussion
The endothermic peak centered at T ≈ 578 K in the
DTA thermogram, Fig. 8, is considered as an indication
of the existence of a structural phase transition at this
temperature, specially where there is no practically any
loss in the weight of the sample at that temperature as
given in reference [1]. Therefore, the anomalies found in
the measured electrical parameters, around T ≈ 580 K,
are a reflection of the structural phase transition and not
due to the change in the conduction mechanism. This
transition is of the order — disorder type, i.e., it is due
to the disorder of the ClO4 group. Further details are
given elsewhere [2]. This is in good agreement with previous work [1, 2]. The higher values of ε0 and/or ε00 in
the transition temperature region may suggest the existence of Ferro electricity. For this reason, a usual circuit for testing such possibility was used. However, the
test was found to be negative. Thus, the possibility of
a ferroelectric phase transition has been excluded in the
present work since there is no evidence for the formation of hysteresis loops over the investigated temperature
range. Thus the higher values of ε0 and ε00 is therefore
due to the surface polarization effect [2] rather than Ferro
electricity. One can summarize the phase transition as
follows:
Regarding the conduction mechanism, it is known that,
there are three distinct processes [26] that have been proposed; namely, quantum mechanical tunneling (QMT)
through the barrier, classical hopping over the barrier
(CBH) and small polaron tunneling (SPT). The expression for AC conductivity due to (QMT) is given by [27]:
= 1 − 6kT /{Eo − kT ln(1/ωτ )} .
(8)
and for small polaron [16]
s = 1 − 4/[ln(1/ωτ ) − WH /kT ]
(9)
The symbols take their usual meanings. k is Boltzmann’s
constant, T — absolute temperature, Eo — optical energy gap, ω — angular frequency, υph and τ (τ = 1/υph )
are the phonon frequency and the relaxation time respectively, and WH is the activation energy involved on the
electron transfer process between a pair.
From Eqs. (6) and (7) for QMT model, it is clear that
the value of s is temperature independent whereas, for
hopping model, Eq. (8), the value of s decreases with
increasing temperature and less dependent on the frequency, and finally, Eq. (9) predict that s increases as T
increases.
Figure 6 indicates that the value of s decreases with
increasing temperature. This means that, in the investigated temperature region, the data confirm the hopping
model (CBH).
Figure 7 shows an increasing of A(T ) as the temperature increases which means the polarizablity increases as
temperature increases.
4. Conclusions
The present work represents the first report on AC conductivity and permittivity on the polycrystalline sample
of KClO4 . The data confirm the existence of a structural
phase transition at T ≈ 575 K. Moreover, the absence of
ferroelectric hystersis loops gives strong evidence that the
structural transition is not associated with a ferroelectric
phase change. Another important point of interest is the
use of the power law in the analysis of our data where the
conduction mechanism is found to occur via the hopping
over the barrier model (CBH).
References
[1] M.M. Abdel-Kader, M.M. Mosaad, M.A. Fahim,
K.K. Tahoon, Z.H. El-Tanahy, Phase Transitions 62,
105 (1997).
[2] T. Shripathi, H.L. Bhat, P.S. Narayanan, Phys. Stat.
Sol. A 126, 511 (1975).
[3] B. Dicken, Acta Cryst. B 25, 1875 (1969).
[4] A.K. Jain, G.C. Upreti, Solid State. Comm. 28, 571
(1978).
[5] J.O. Lundgreen, Acta Cryst. B 35, 1027 (1979).
940
H.M. Abdelmoneim
[6] B.B. Berglund, R. Tellgren, J.O. Thomas, Acta
Cryst. B 32, 2444 (1976).
[7] J.O. Lundgreen, Acta Cryst. B 36, 1774 (1980).
[8] A. Sequeira, C. Bernal, Acta Cryst. B 31, 1735
(1975).
[9] G. Chiari, G. Ferraris, Acta Cryst. B 38, 2331 (1982).
[10] A. Sequeira, I. Bernal, Acta Cryst. B 31, 1735 (1975).
[11] E. Price, B. Dickens, J.J. Rush, Acta Cryst. B 30,
1167 (1974).
[12] C.A. Blackburn, J.C. Gallucci, E.R. Gerkin,
J.W. Reppart, Acta Cryst. C 49, 1437 (1993).
[13] C.A. Blackburn, E.R. Gerkin, Acta Cryst. C 49, 1439
(1993).
[14] M.M. Abdel-Kader, H.M. Naguib, H.M. Abdel-Moneim, M.A. Fahim, Phase Trans. A Multinational
Journal, 78, 621 (2005).
[15] A.K. Jonsher, Dielectric Relaxation in Solids, Chelsea
dielectric press, London 1983.
[16] R.H. Chin, R.Y. Chang, C.S. Shern, T. Fukami,
J. Phys. Chem. Sol. 64, 553 (2003).
[17] K. Funke, Prog. Solid State Chem. 22, 111 (1993).
[18] H. Jain, J.N. Mundy, J. Non-Cryst. Solids 91, 315
(1987).
[19] N.F. Mott, E.A. Davis, Electronic Progresses in non-crystalline Solids, Clarendon Press, Oxford, (1970).
[20] J.C. Dyre, T.B. Schroder, Rev. Mod. Phys. 72, 873
(2000).
[21] S.R. Elliott, Solid State Ionics 27, 131 (1988).
[22] R.H. Chin, R.Y. Chang, C.S. Chern, J. Phys. Chem.
Sol. 63 (2002).
[23] R.H. Chin, R.J. Wang, T.M. Chen, C.S. Shen,
J. Phys. Chem. Sol. 61, 519 (2000).
[24] W.K. Lee, J.F. Liu, A.S. Nowick, Phys. Rev. Lett. 67,
1559 (1991).
[25] S.R. Elliott, A.P. Owens, Phil. Mag. 60, 777 (1989).
[26] S.R. Elliott, Adv. Phys. 36, 135 (1987).
[27] I.G. Austin, N.F. Mott, Adv. Phys. 18, 41 (1969).
[28] A.K. Jonsher, J. Mater. Sci. 13, 553 (1978).
[29] C. Karthik, V.B.R. Varma, J. Phys. Chem. Sol. 67,
2437 (2006).